Surely if the patient has a justified concern about their safety then that's rational decision making rather than clinical anxiety. Anxiety in a medical sense isn't the same as being scared or worried (though the strain of fear and worry can contribute to developing anxiety). I'd say an essential feature of clinical anxiety is that it's a disproportionate response to the situation. Knowing that it makes no sense is part of what makes it so frustrating, often creating a vicious circle of increasing stress.
An employee who has legitimate safety concerns at work should seek the support of their trade union rather than their doctor.